The metaphor of the mental number line accounts for numerous empirical effects of spatial-numerical associations. In the present study, we aimed at investigating directional spatial-numerical associations reflected by SNARC-like digit-direction and sign-direction congruency effects as well as the sign-digit compatibility effect when 6th graders…

Children in third and fourth grades suffering from developmental dyscalculia (DD) and typically developing children were asked to compare numbers to a standard. In two separate blocks, they were asked to compare a number between 1 and 9 to 5, or a two-digit number between 10 and 99 to 55. In the single-digit comparisons, DD children were…

Children's mental performance was studied in the context of arithmetic word problem solution. Response latency and error data indicated subtraction was more difficult than addition. Understanding children's problem solutions in terms of flexible strategy use and the fact that many errors have a systematic basis are important in studying children's…

Research recurrently indicates that children who have difficulty with arithmetic often use systematic routines that yield wrong answers. Recent research has focused less on identifying the most common errors among groups of children and more on analyzing individual children's errors. This paper considers the source of systematic errors in…

The informal subtraction strategies that children develop are discussed in detail, with the role of the counting-down strategy described. Problems and remedies for difficulties caused by counting backward and the double count are also presented. (MNS)

This experiment involved 176 London children aged six and seven. Their levels of attainment on subtraction were quickly and accurately established by two questions. Then teaching programs were used to help them attain prerequisite skills. To symbolize too soon is a danger to be avoided. (MNS)

A model of subtraction development and the computing difficulties and research issues suggested by the model are outlined. Demands of simultaneous processes, difficulties with informal subtraction, and the impact on the counting-up procedure are discussed. (MNS)

Teaching sequences designed to develop strategies for comparing numerals in grade two (in France) were analyzed. Children's strategies were noted, and an experiment confirmed underlying misconceptions concerning number. (MNS)

Dialogue from an interview with a child about division basic facts is presented. The facts are considered by groups, and specific errors are noted. Finally, remediation ideas are given. (MNS)

Forty-three first-grade children, who had received no formal instruction in addition and subtraction, were individually administered 20 problems that could be solved using addition or subtraction. The problems were selected to represent the following semantic types: joining, separating, part-part-whole, comparison, and equalizing. Responses were…

The need to provide understandable problems and ways to help children understand problems are explored. An interview with a sixth grader depicts his incorrect strategies and leads to suggestions for teaching problem solving using a range of mathematical models for each operation. (MNS)

This study was designed to follow up earlier work on mapping instruction. The two main goals were to: (1) test the effectiveness of mapping instruction as a general cure for "buggy" subtraction algorithms, and (2) explore two alternative explanations of how this new form of instruction works. It was hypothesized that mapping cures bugs…

The process of transition from a novice's state to that of an expert, in the domain of decimals, is described in terms of explicit, intermediate, and transitional rules which are consistent yet erroneous. Data from students in grades 6-9 are included. (MNS)

The Concepts in Secondary Mathematics and Science (CSMS) and Strategies and Errors in Secondary Mathematics (SESM) research projects based at Chelsa College, England, have shown the marked reluctance of secondary school students to use fractions when solving mathematical problems, even though they have been taught the topic for a number of years.…

Recent research on solving addition and subtraction word problems has resulted in the construction of theoretical models of children's problem-solving processes. Some of these models have been translated into computer programs. Characteristics and predictions of the theoretical analysis developed by Riley, Greeno, and Heller (1983) are discussed…